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Irrational Numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...

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Q: Which irrational number is closest to 6?

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6.000........

Irrational numbers are infinitely dense. Between any two numbers, there are infinitely many irrational numbers. So if it was claimed that some irrational, x, was the closest irrational to 6, it is possible to find an infinite number of irrationals between 6 and x. Each one of these infinite number of irrationals would be closer to 6 than x. So the search for the nearest irrational must fail.

There is no such number. Between any two irrational numbers there are infinitely many irrational numbers. So, the claim that x is the irrational number closest to ten can be demolished by the fact that there are infinitely many irrational numbers between x and 10 (or 10 and x).

First - 50 is a rational number, not an irrational number since it can be represented as a ratio of integers, i.e. 50/1 With that said: the two integers closest to it are 49 and 51

The set of irrational numbers is infinitely dense. As a result there are infinitely many irrational numbers between any two numbers. So, if any irrational number, x, laid claim to be the closest irrational number to 3, it is possible to find infinitely many irrational numbers between x and 3. Consequently, the claim cannot be valid.

18 and 20

They are the integer part of the irrational number and the successor to that integer. Thus, for pi, the two integers are 3 and 4.

Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.

Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)

irrational

6 is a rational number.

it is irrational because it's from the exponential numbers

no it is not irrational irrational is a neverending number like2.36945856235......... that goes on and on 6 over 7 is a rational number rational numbers are whole numbers natural numbers and integers.

-6 is rational, as it can be written as 1/b (-6/1). An example of an irrational number is pi, as it has an infinite amount of decimal places.

It is an irrational number.

The square root of 240 is irrational; the closest number depends upon how many decimal places you want. If you want the closest whole number then: √240 = 15.49193... → closest whole number is 15.

no

e, √8, pi, √10

No

Rational.

No.

It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.

No, 3.56 is not an irrational number. 3.56 is rational.

6/5 is a rational number

The square root of 61.93 is irrational. Since rational numbers are infinitely dense there cannot be a closest rational.